Which disease is a progressive, degenerative disease of the brain that ultimately results in dementia and is associated with a shortage of acetylcholine?

Alzheimer's disease.

Explanation:

Alzheimer's is the neuro degenerative disorder in which the nerve cells of the body starts digressed or destroyed. This disease also cause dementia that causes the loss of thinking and memory ability.

This disorder shows early symptoms like forgetting the events and small memory. This disease becomes worst with the increasing age. The neurotransmitter causes the decrease in acetylcholine neurotransmitter that plays an important role in the chemical signal transmission.

Thus, the answer is Alzheimer's disease.